STAT 467 Rensselaer Polytechnic Institute Statistics Questions

Stat 467 Homework 1
Due on Tuesday, 2/15 by 11:59pm EST
1. We would like to conduct an analysis on a subset of MNIST data with digits from 0 to 4
only. Without running the code in Python, describe the architecture for the following
deep learning model, including number of layers, number of units in each layer (layer
width), number of parameters in each layer (show the details of calculations).
network.mlp = models.Sequential()
network.mlp.add(layers.Dense(1024, activation=’relu’, input_shape=(28 * 28,)))
network.mlp.add(layers.Dense(512, activation=’relu’))
network.mlp.add(layers.Dense(256, activation=’relu’, kernel_regularizer=regularizers.l1(0.001)))
network.mlp.add(layers.Dense(5, activation=’softmax’))
2. Consider the following two-layer network.
The weights and bias for X1(1) is (5,-3) and 2, respectively. The weights and bias for X2(1) is
(-2,6) and -1, respectively. The weights and bias for Y are (1,1) and 1, respectively. The
activation function is ReLU for X1(1) and X2(1) and identity function for Y. We have two
data points: (x11=1, x12=1, y1=5) and (x21=1, x22=-1, y2=8).
(a) Calculate the prediction for two data points using the above network. Calculate the
total square loss value. Show the details for your calculation.
(b) Now we add a dropout with rate 0.5 to the first hidden layer. Assume X2(1) is
dropped when making the prediction for data point (x11=1, x12=1,y1=5) and X1(1) is
dropped when making the prediction for data point (x21=1, x22=-1,y2=8). Calculate
the prediction for two data points and the total square loss value. Show the details
for your calculation.
3. Conduct the analysis on MNIST data using multi-layer neuron networks (treating each
image as a vector). Tune all hyper-parameters that you think matter. Report your best
model and accuracy on the test set. Show the details of your tuning process. Submit
your complete code in notebook style (same as colab illustrated in class).

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